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Chapter 13: Risk and Capital Budgeting
13-11
8. Coefficient of variation (LO1) Five investment alternatives have the following returns and
standard deviations of returns.
Alternative
Returns:
Expected Value
Standard
Deviation
A .....................................
$ 1,000
$ 590
B .....................................
3,000
600
C .....................................
3,000
750
D .....................................
5,000
2,300
E .....................................
10,000
800
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.
13-8. Solution:
Coefficient of variation (V) = standard deviation/expected value
Ranking from
lowest to highest
A
$590/$1,000 = .59
E (.08)
B
$600/$3,000 = .20
B (.20)
C
$750/$3,000 = .25
C (.25)
D
$2,300/$5,000 = .46
D (.46)
E
$800/$10,000 = .08
A (.59)
9. Coefficient of variation (LO1) In problem 8, if you were to choose between Alternatives
B and C only, would you need to use the coefficient of variation? Why?
13-9. Solution:
expected return.
Chapter 13: Risk and Capital Budgeting
13-12
10. Coefficient of variation and time (LO1) Sensor Technology wishes to determine its
coefficient of variation as a company over time. The firm projects the following data
(in millions of dollars):
Year
Profits:
Expected Value
Standard
Deviation
1 ....................................
$ 90
$ 31
3 ....................................
120
52
6 ....................................
150
83
9 ....................................
200
146
a. Compute the coefficient of variation (V) for each time period.
b. Does the risk (V) appear to be increasing over a period of time? If so, why might this
be the case?
13-10. Solution:
Sensor Technology
a.
Year
Profits:
Expected Value
Standard
Deviation
Coefficient
of Variation
1
90
31
.34
3
120
52
.43
6
150
83
.55
9
200
146
.73
11. Risk-averse (LO2) Tim Trepid is highly risk-averse while Mike Macho actually enjoys
taking a risk.
a. Which one of the four investments should Tim choose? Compute coefficients of
variation to help you in your choice.
Investments
Returns:
Expected Value
Standard
Deviation
Buy stocks ...........................
$ 8,800
$ 5,600
Buy bonds ............................
7,000
2,060
Buy commodity futures ........
16,900
22,100
Chapter 13: Risk and Capital Budgeting
13-13
Buy options ..........................
11,600
12,400
b. Which one of the four investments should Mike choose?
13-11. Solution:
Coefficient of variation (V) = standard deviation/expected
value.
Buy stocks $5,600/8,800 = .636
12. Risk-averse (LO2) Wildcat Oil Company was set up to take large risks and is willing to
take the greatest risk possible. Richmond Construction Company is more typical of the
average corporation and is risk-averse.
a. Which of the following four projects should Wildcat Oil Company choose? Compute
the coefficients of variation to help you make your decision.
b. Which one of the four projects should Richmond Construction Company choose
based on the same criteria of using the coefficient of variation?
Projects
Returns:
Expected Value
Standard
Deviation
A............................................
$262,000
$138,000
B ............................................
674,000
403,000
C ............................................
88,000
108,000
D............................................
125,000
207,000
13-12. Solution:
Chapter 13: Risk and Capital Budgeting
13-14
Wildcat Oil Company and
Richmond Construction Company
Coefficient of variation (V) = standard deviation/expected value
Project A $138,000 / 262,000 = .527
13. Coefficient of variation and investment decision (LO1) Kyle’s Shoe Stores, Inc., is
considering opening an additional suburban outlet. An aftertax expected cash flow of $100
per week is anticipated from two stores that are being evaluated. Both stores have positive
net present values.
Which store site would you select based on the distribution of these cash flows? Use
the coefficient of variation as your measure of risk.
Site A
Site B
Probability
Cash Flows
Probability
Cash Flows
.2
50
.1
20
.3
100
.2
50
.3
110
.4
100
.2
135
.2
150
.1
180
13-13. Solution:
Kyle’s Shoe Stores, Inc.
Standard Deviations of Sites A and B
Site A
Chapter 13: Risk and Capital Budgeting
13-15
D
D
(D D)−
2
(D D)−
P
2
(D D)−
P
$ 50
$100
$–50
$2,500
.2
$500
100
100
–0–
–0–
.3
–0–
110
100
+10
100
.3
30
135
100
+35
1,225
.2
245
$775
A775 $27.84
==
13-13. (Continued)
Site B
D
D
(D D)−
2
(D D)−
P
2
(D D)−
P
$ 20
$100
$–80
$6,400
.1
$ 640
50
100
–50
2,500
.2
500
100
100
–0–
–0–
.4
–0–
150
100
+50
2,500
.2
500
180
100
+80
6,400
.1
640
$2,280
B2,280 $47.75
==
Site A is the preferred site since it has the smallest coefficient of
Chapter 13: Risk and Capital Budgeting
13-16
14. Risk-adjusted discount rate (LO3) Micro Systems is evaluating a $50,000 project with
the following cash flows.
Year
Cash Flows
1......................
$ 9,000
2......................
12,000
3......................
18,000
4......................
16,000
5......................
24,000
The coefficient of variation for the project is .726.
Based on the following table of risk-adjusted discount rates, should the project be
undertaken? Select the appropriate discount rate and then compute the net present value.
Coefficient Discount
of Variation Rate
0 – .25 ................... 6%
.26 – .50 ................... 8
.51 – .75 ................... 12
.76 – 1.00 ................. 16
1.01 – 1.25 ................ 20
13-14. Solution:
Micro Systems
Year
Inflows
PVIF @ 12%
PV
1
$ 9,000
.893
$ 8,037
2
12,000
.797
9,564
3
18,000
.712
12,816
4
16,000
.636
10,176
5
24,000
.567
13,608
PV of Inflows
$54,201
Investment
50,000
NPV
$ 4,201
Based on the positive net present value, the project should be
undertaken.
Chapter 13: Risk and Capital Budgeting
13-17
15. Risk-adjusted discount rate (LO3) Payne Medical Labs is evaluating two new products
to introduce into the marketplace. Product 1 (a new form of plaster cast) is relatively low in
risk for this business and will carry a 10 percent discount rate. Product 2 (a knee joint
support brace) has a less predictable outcome and will require a higher discount rate of 15
percent. Either investment will require an initial capital outlay of $90,000. The inflows
from projected business over the next five years are given below. Which product should be
selected using net present value analysis?
Years
Product 1
Product 2
1 .....................
$25,000
$16,000
2 .....................
30,000
22,000
3 .....................
38,000
34,000
4 .....................
31,000
29,000
5 .....................
19,000
70,000
13-15. Solution:
Payne Medical Labs
Product 1 Product 2
Year
Inflows
PVIF
@
10%
PV
Year
Inflows
PVIF
@
15%
PV
1
$25,000
.909
$ 22,725
1
$16,000
.870
$ 13,920
2
30,000
.826
24,780
2
22,000
.756
16,632
3
38,000
.751
28,538
3
34,000
.658
22,372
4
31,000
.683
21,173
4
29,000
.572
16,588
5
19,000
.621
11,799
5
70,000
.497
34,790
PV of Inflows
$109,015
$104,302
Investment
90,000
90,000
NPV
$ 19,015
$ 14,302
Select Method 1
higher discount rate.
Chapter 13: Risk and Capital Budgeting
13-18
16. Discount rate and timing (LO1) Fill in the table below from Appendix B. Does a high
discount rate have a greater or lesser effect on long-term inflows compared to recent ones?
Discount Rate
Years
6%
18%
1...........................
_______
_______
10...........................
_______
_______
20...........................
_______
_______
13-16. Solution:
Discount Rate
Years
6%
18%
1
.943
.847
10
.558
.191
20
.312
.037
17. Expected value with net present value (LO1) Debby’s Dance Studios is considering the
purchase of new sound equipment that will enhance the popularity of its aerobics dancing.
The equipment will cost $25,000. Debby is not sure how many members the new
equipment will attract, but she estimates that her increased annual cash flows for each of
the next five years will have the following probability distribution. Debby’s cost of capital
is 11 percent.
Cash Flow
Probability
$3,600 .............
.2
5,000 .............
.3
7,400 .............
.4
9,800 .............
.1
a. What is the expected value of the cash flow? The value you compute will apply to
each of the five years.
b. What is the expected net present value?
c. Should Debby buy the new equipment?
Chapter 13: Risk and Capital Budgeting
13-19
13-17. Solution:
Debby’s Dance Studios
a. Expected Cash Flow
Cash Flow P
$3,600
×
.2
$ 720
5,000
×
.3
1,500
7,400
×
.4
2,960
9,800
×
.1
980
$6,160
b. Net Present Value (Appendix D)
$6,160 × 3.696 (PVIFA @ 11%, n = 5) =
18. Deferred cash flows and risk-adjusted discount rate Highland Mining and Minerals Co.
is considering the purchase of two gold mines. Only one investment will be made. The
Australian gold mine will cost $1,600,000 and will produce $300,000 per year in years 5
through 15 and $500,000 per year in years 16 through 25. The U.S. gold mine will cost
$2,000,000 and will produce $250,000 per year for the next 25 years. The cost of capital is
10 percent.
a. Which investment should be made? (Note: In looking up present value factors for this
problem, you need to work with the concept of a deferred annuity for the Australian
mine. The returns in years 5 through 15 actually represent 11 years; the returns in
years 16 through 25 represent 10 years.)
b. If the Australian mine justifies an extra 5 percent premium over the normal cost of
capital because of its riskiness and relative uncertainty of cash flows, does the
investment decision change?
Chapter 13: Risk and Capital Budgeting
13-20
13-18. Solution:
Highland Mining and Minerals Co.
a. Calculate the net present value for each project.
The Australian Mine
Years
Cash
Flow
n Factor
PVIFA@10%
Present
Value
5–15
$300,000
(15 – 4)
(7.606 – 3.170)
$1,330,800
16–25
$500,000
(25 – 15)
(9.077 – 7.606)
$ 735,500
Present Value of inflows $2,066,300
Present Value of outflows $1,600,000
Net Present Value $ 466,300
13-18. (Continued)
The U.S. Mine
Years
Cash Flow
n Factor
PVIFA@10%
Present
Value
1–25
$250,000
(25)
9.077
$2,269,250
